One big question become ease of use and reliability. While TVs certainly have built in streaming functionality these days, there are huge questions as to the reliability and quality of the internal streaming devices in the different displays, and bigger question marks as to how reliable playback is from these units, and still further questions of how easy it will be to turn on, setup a playback stream, and have it run for the entire day.
On a budget, this is basically free from what you've described. Network connection to the TV, run it back to your networked PC, and set up all the streaming videos and connections to the TV. The issue, IMO, is that this is very limited and will be complex to not only setup, but to continue to use day-in and day-out.
Better would be a HDBaseT run to every TV for HDMI connectivity and a small HDMI matrix switcher connected to the various sources. You can set it up to play back from any HDMI enabled source such as HD cable, AppleTV, computers, etc. A small 8x8 HDMI matrix is about $2,000 for an inexpensive model. A small 4x4 version is less than half that. HDBaseT transmitter/receiver pairs are about $500 for very good ones, and $200 for cheaper, and potentially less reliable units, but the same video quality.
A best scenario would be to then install a control system to run the show with iPad control. Your dad could pick up the iPad and press a 'System On' button and all the TVs would power on, all equipment would switch to the proper inputs, and sound would start up with a couple of guided button presses. From there, switching and control for each TV could be individually available. This is the most professional way of doing things and provides long term reliability and ease of use, but carries the highest price tag because there is additional installation and custom programming and some extra gear.